本程序实现有关二叉树的递归算法，包括

1．求二叉树的层次(高度)

2．求二叉树的叶子个数

3．求二叉树的总结点个数

4．求二叉树的度为1的结点个数

5．求二叉树的度为2的结点个数

6．复制二叉树

7．交换二叉树的左右子树

8．利用先序序列建立二叉链表存储的二叉树

(二)基本要求

1．用二叉链表的形式存储二叉树

2．利用C的图形功能显示二叉树形态 为蓝底白树

#include

#include

#include

#include

#include

#define OK 1

#define ERROR 0

#define OVERFLOW -2

#define NULL 0

typedef int Status;

typedef char TElemType;

typedef struct BiTNode{

TElemType data;

struct BiTNode *lchild,*rchild;

}BiTNode,*BiTree;

Status CreateBiTree(BiTree

*T) //先序创建二叉树

{ char data;

scanf("%c",&data);

if(data=='#') *T=NULL;

else {

*T=(BiTree)malloc(sizeof(BiTNode));

if(!(*T)) exit(OVERFLOW);

(*T)->data=data;

CreateBiTree(&(*T)->lchild);

CreateBiTree(&(*T)->rchild);

}

return

OK;

}

Status DestroyBiTree(BiTree

*T) //销毁二叉树 释放内存

{ if((*T)->data==NULL)return

ERROR;

free(*T);

*T=NULL;

return OK;

}

void Paint(BiTree T,int x,int y,int

g) //

打印二叉树树形(递归实现)

{ char c[2];

int you=0,zuo=0;

if(T)

{setcolor(WHITE);

circle(x,y,10);

c[0]=T->data;

c[1]='\0';

outtextxy(x,y,c);

if(T->lchild!=NULL)

{if(x>g)

zuo=(x-g)/2+g;

if(x

line(x-1,y,zuo,y+80);

}

if(T->rchild!=NULL)

{you=2*x-zuo;

line(x-1,y,you,y+80);

}

Paint(T->lchild,zuo,y+80,x);

Paint(T->rchild,you,y+80,x);

}

}

int level(BiTree

T) //求二叉树的层次(高度)

{

int l1,l2;

if(T==NULL) return 0;

else{l1=level(T->lchild);

l2=level(T->rchild);

return l1>l2?l1+1:l2+1;

}

}

int leaf(BiTree

T) //求二叉树的叶子节点数

{

int n1,n2;

if(T==NULL) return 0;

else

if(T->lchild==NULL&&T->rchild==NULL)return

1;

else {n1=leaf(T->lchild);

n2=leaf(T->rchild);

return n1+n2;

}

}

int nodes(BiTree

T) //求二叉树的总节点数

{

int n1,n2;

if(T==NULL) return 0;

else

if(T->lchild==NULL&&T->rchild==NULL)return

1;

else {n1=nodes(T->lchild);

n2=nodes(T->rchild);

return n1+n2+1;

} }

int node1(BiTree

T) //求度为一的节点数目

{

int n1,n2,n=0;

if(T==NULL) return 0;

else {

if(T->lchild&&T->rchild==NULL||T->lchild==NULL&&T->rchild)

n=1;

n1=node1(T->lchild);

n2=node1(T->rchild);

return n1+n2+n;

}

}

int node2(BiTree

T) //求度为二的节点数目

{

int n=0,n1,n2;

if(T==NULL) return 0;

else {

if(T->lchild&&T->rchild)

n=1;

n1=node2(T->lchild);

n2=node2(T->rchild);

return n+n1+n2;

}

}

void Copy(BiTree T,BiTree

*T2) //复制二叉树

{

if(T==NULL) *T2=NULL;

else{*T2=(BiTree)malloc(sizeof(BiTNode));

(*T2)->data=T->data;

Copy(T->lchild,&(*T2)->lchild);

Copy(T->rchild,&(*T2)->rchild);

}

}

void exchange(BiTree

*T) //交换二叉树的所有左右子树

{

BiTNode *t;

if(*T)

{t=(*T)->lchild;

(*T)->lchild=(*T)->rchild;

(*T)->rchild=t;

exchange(&(*T)->lchild);

exchange(&(*T)->rchild);

}

}

main()

{

BiTree T,T2; int x,y,g;

int gdriver,gmode;

int d,yezi,jiedian,dian1,dian2;

x=320;y=30; g=0;

gdriver=DETECT;

printf("input the BiTree's data(in PreOrder and

<=63ge):\n"); //创建

if(!CreateBiTree(&T))printf("kongjian OVERFLOW! can

not create!\n");

else printf("cunchu success!\n");

printf("press any key to contunue:\n");

getch();

printf("level of the tree is

:\n"); //求层数

d=level(T);

printf("%d\n",d);

printf("\n press any key to continue:\n");

getch();

printf("leaf number of the tree is

:\n"); //求叶子

yezi=leaf(T);

printf("%d\n",yezi);

printf("\n press any key to continue:\n");

getch();

printf("nodes number of the tree is

:\n"); //求总节点

jiedian=nodes(T);

printf("%d\n",jiedian);

printf("\n press any key to continue:\n");

getch();

printf("du wei 1 d jiedian node1 of the tree is

:\n"); //求度为一的节点数 dian1=node1(T);

printf("%d\n",dian1);

printf("\n press any key to continue:\n");

getch();

printf("node2 of the tree is

:\n"); //求度为二的节点

dian2=node2(T);

printf("%d\n",dian2);

printf("\n press any key to continue:\n");

getch();

printf("Now copy the

tree:\n"); //复制树

Copy(T,&T2);

printf("\n press any key to continue:\n");

getch();

printf("now,print the BiTree like a

tree:\n"); //打印树

printf("press any key to see the tree:\n");

getch();

initgraph(&gdriver,&gmode,"C:\\TC");

setbkcolor(BLUE);

cleardevice();

Paint(T,x,y,g);

getch();

closegraph();

printf("press any key to continue:\n");

getch();

printf("Now change the tree d right and

left:\n"); //交换左右子树

exchange(&T);

printf("\n press any key to continue:\n");

getch();

printf("now,print the BiTree like a tree:\n");

printf("press any key to see the

tree:\n"); //打印树形以确认交换

getch();

initgraph(&gdriver,&gmode,"C:\\TC");

setbkcolor(BLUE);

cleardevice();

Paint(T,x,y,g);

getch();

closegraph();

printf("press any key to continue:\n");

getch();

if(DestroyBiTree(&T))printf("the BiTree

destroyed!\n"); //销毁树

else printf("NULL!can not destroy!\n");

printf("press any key to

continue:\n"); //结束程序

getch();

}